Here, to minimize the source transmit power \(\sum _{m\in \mathbb {M}} P_m\)  for high energy-efficiency [1]}, [2]}, we first determine the precoding vector \(\mathbf {v}_m\)  that maximizes the received SNR \(\gamma _m\triangleq \frac{P_m G_{\mathrm {s}}|\mathbf {h}^*(\mathbf {q}, {\mathbf {\rho }}_m) \mathbf {\Theta } \mathbf {H}(\mathbf {q})\mathbf {v}_m|^2}{\sigma ^2}\)  of UAV-BS \(m\)  for fixed \(P_m\) , which leads to a smaller transmit power while achieving the same rate. Lemma REF  presents the result.
